A Treatise on Trigonometry, Plane and Spherical: With Its Application to Navigation and Surveying, Nautical and Practical Astronomy and Geodesy : with Logarithmic, Trigonometrical, and Nautical Tables, for the Use of Schools and CollegesG.P. Putnam, 1851 - 372 pages |
From inside the book
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Page x
... radius for homogeneity , Examples in the solution of right - angled triangles , ib . 57 ib . Exercises in ditto , 59 Practical examples , 60 Practical exercises , ib . Use of the arithmetical complement , 61 SOLUTION OF OBLIQUE ANGLED ...
... radius for homogeneity , Examples in the solution of right - angled triangles , ib . 57 ib . Exercises in ditto , 59 Practical examples , 60 Practical exercises , ib . Use of the arithmetical complement , 61 SOLUTION OF OBLIQUE ANGLED ...
Page xix
... radius of curvature in terms of the 365 latitude , 366 Demonstration of formula for determining the figure and dimensions of the earth by the lengths of two measured degrees in distant latitudes , ib . Prime vertical transit , 368 ...
... radius of curvature in terms of the 365 latitude , 366 Demonstration of formula for determining the figure and dimensions of the earth by the lengths of two measured degrees in distant latitudes , ib . Prime vertical transit , 368 ...
Page 4
... radius included between the sides of another angle , the first angle is double , triple , or sextuple the second . The relative magnitudes of angles may therefore be correctly expressed by means of the relative magnitudes of the arcs ...
... radius included between the sides of another angle , the first angle is double , triple , or sextuple the second . The relative magnitudes of angles may therefore be correctly expressed by means of the relative magnitudes of the arcs ...
Page 5
... , and extending from side to side of the angle , may be with any radius at pleasure . * Having the same centre . This may be distinctly seen in the following diagram . MEASUREMENT OF ANGLES . 5 Measurement of angles,
... , and extending from side to side of the angle , may be with any radius at pleasure . * Having the same centre . This may be distinctly seen in the following diagram . MEASUREMENT OF ANGLES . 5 Measurement of angles,
Page 6
... radius also con- tains 50 degrees , and so would an are included between the sides of the given angle de- scribed with any other radius whatever . Where the size of an angle is 6 B 50 이 56 이 10 a 150 १० 20 20 10 A over , such that ...
... radius also con- tains 50 degrees , and so would an are included between the sides of the given angle de- scribed with any other radius whatever . Where the size of an angle is 6 B 50 이 56 이 10 a 150 १० 20 20 10 A over , such that ...
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Common terms and phrases
altitude applied azimuth called centre colatitude collimation column comp computed correction cosē cosc cosec cosine cotangent course declination deduced determined diagram diff difference of latitude difference of longitude divided equal equation error EXAMPLE expressed formula Geom Greenwich hence horizontal hour angle hypothenuse instrument intersection limb logarithm longitude means measured meridian middle wire miles multiplied Napier's rules Nautical Almanac number of degrees object observed obtained parallax parallel passing perpendicular plane sailing plane triangle pole proportion quadrant radius refraction right angled triangle right ascension sailing screw secant second member semidiameter ship side opposite siderial sin a sin sinē sine sine and cosine sine of half solution sphere spherical triangle spirit level star subtracting supporting axis tangent telescope theodolite transit trigonometrical lines vernier vertical circle zenith distance
Popular passages
Page 204 - ... 6. The latitude of a place is its distance north or south of the equator, measured on the meridian of the place.
Page 136 - The sine of half the sum of two angles of a spherical triangle is to the sine of half their difference as the tangent of half the interjacent side is to the tangent of half the difference of the other two sides.
Page 33 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 86 - When a ray of light passes from one medium to another, it is refracted so that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities in the two media.
Page 79 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 66 - FH is the sine of the arc GF, which is the supplement of AF, and OH is its cosine ; hence, the sine of an arc is equal to the. sine of its supplement ; and the cosine of an arc is equal to the cosine of its supplement* Furthermore...
Page 219 - Then, along the horizontal line, and under the given difference of latitude, is inserted the proper correction to be added to the middle latitude to obtain the latitude in which the meridian distance is accurately equal to the departure. Thus, if the middle latitude be 37°, and the difference of latitude 18°, the correction will be found on page 94, and is equal to 0° 40'. EXAMPLES. 1. A ship, in latitude 51° 18...
Page 213 - A2,lay off the distance BC = 23 miles; in the direction parallel to A3, lay off CD = 36 ; in the direction parallel to A4, lay off DE = 12 miles ; and, lastly, in the direction parallel to A5, lay off EF = 41 ; then F will be the place of the ship at the end of the traverse ; consequently, AF will be the distance made good, and the angle FAS the direct course ; applying, therefore, the distance AF to the scale of equal parts, we shall find it reach from 0 to 62| ; and applying the distance Sa to...
Page 284 - ZP. Now, in the triangle PSS', we have given two sides and the included angle to find the third side SS', and one of the remaining angles, say the angle PSS'.
Page 13 - SINE of an arc, or of the angle measured by that arc, is the perpendicular let fall from one extremity of the arc, upon the diameter passing through the other extremity. The COSINE is the distance from the centre to the foot of the sine.